1. In Buckingham n theorem, if n is the number of variables and m is the number of basic dimensions, the number of independent dimensionless parameters would be, A. (m-n) B. (n-m) C. (m + n) D. (n/m) 2. Which is a dimensionless parameter? B. Angular Velocity D. Density A. Froude Number c. Viscosity
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- 1. In Buckingham π theorem, if n is the number of variables and m is the number of basic dimensions, the number of independent dimensionless parameters would be,A. (m – n) B. (n – m) C. (m + n) D. (n/m)Books on porous media and atomization claim that the viscosityμ and surface tension Y of a fl uid can be combinedwith a characteristic velocity U to form an important dimensionlessparameter. ( a ) Verify that this is so. ( b ) Evaluatethis parameter for water at 20°C and a velocity of3.5 cm/s. Note: You get extra credit if you know the nameof this parameter.The kinematic viscosity of a liquid is 0.058 cm^2/s and has a density of 500 kg/m^3. What is the absolute viscosity in poise
- The Ekman number, Ek, arises in geophysical fluiddynamics. It is a dimensionless parameter combining seawaterdensity ρ , a characteristic length L , seawaterviscosity μ , and the Coriolis frequency Ω sin φ , where Ωis the rotation rate of the earth and φ is the latitude angle.Determine the correct form of Ek if the viscosity is in thenumerator.The Archimedes number, Ar, used in the flow of stratifiedfluids, is a dimensionless combination of gravity g , densitydifference Δ ρ , fluid width L , and viscosity μ . Find theform of this number if it is proportional to g .Here, a 1:10 scale prototype of a propeller on a ship is to be tested in a water channel. What would the rotating speed of the model be if the rotational speed of the p propeller is 2000 rpm, and if: (a) the Froude number governs the model-prototype similarity(b) Reynolds number governs the similarity
- FLUID MECHANICS final answer mus be in 4 decimal places If the viscosity of water at 70°C is 0.42 centipoise and its relative density is 0.978, determine its absolute viscosity is Pa-s and its kinematics viscosity in m²/s and in stokes.At a sudden contraction in a pipe the diameter changes from D, to D2. The pressure drop, Ap, which develops across the con- traction is a function of D, and Dz, as well as the velocity, V, in the larger pipe, and the fluid density, p, and viscosity, u. Use D, V, and u as repeating variables to determine a suitable set of dimensionless parameters. Why would ti be incorrect to include the velocity in the smaller pipe a sa nadditional variable?1. A lead cube has a total mass of 64 kg. What is the Length of its side in cm? specific gravity of lead = 7.27. 2. If the viscosity of water at 70 degrees celsius is 0.0077 poise and its specific gravity is 0.453, determine its kinematic viscosity in stokes.
- A liquid of density ? and viscosity ? flows by gravity through a hole of diameter d in the bottom of a tank of diameter DFig. . At the start of the experiment, the liquid surface is at height h above the bottom of the tank, as sketched. The liquid exits the tank as a jet with average velocity V straight down as also sketched. Using dimensional analysis, generate a dimensionless relationship for V as a function of the other parameters in the problem. Identify any established nondimensional parameters that appear in your result. (Hint: There are three length scales in this problem. For consistency, choose h as your length scale.) except for a different dependent parameter, namely, the time required to empty the tank tempty. Generate a dimensionless relationship for tempty as a function of the following independent parameters: hole diameter d, tank diameter D, density ? , viscosity ? , initial liquid surface height h, and gravitational acceleration g.Figure shows a gage for very low pressures, inventedin 1874 by Herbert McLeod. ( a ) Can you deduce,from the fi gure, how it works? ( b ) If not, read about it andexplain it to the class.A dimensionless combination of variables that is important in the study of viscous flow through pipes is called the Reynolds number, Re, defined as ???/? where, as indicated in Fig. 11, ? is the fluid density, V the mean fluid velocity, D the pipe diameter, and the fluid viscosity. A Newtonian fluid having a viscosity of 0.38 ? . ?/?² and a specific gravity of 0.91 flows through a 25‐mmdiameter pipe with a velocity of 2.6 ?/?. Determine the value of the Reynolds number using (a) SI units, and (b) BG units.